Sharkovsky theorem
= Sharkovsky theorem
{c}
{wiki=Sharkovsky's_theorem}
Order the positive integers by odd numbers from $3$ upward, then twice the odds, then four times the odds, and so on, followed by descending powers of two and finally $1$. If a continuous interval map has a cycle of one period, it has cycles of every period later in this order. In particular, period three forces every positive period.